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## Chapter #4: Diodes

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**Chapter #4: Diodes**from Microelectronic Circuits Text by Sedra and Smith Oxford Publishing Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**Introduction**• IN THIS CHAPTER WE WILL LEARN • the characteristics of the ideal diode and how to analyze and design circuits containing multiple ideal diodes together with resistors and dc sources to realize useful and interesting nonlinear function • the details of the i-v characteristic of the junction diode (which was derived in Chapter 3) and how to use it to analyze diode circuits operating in the various bias regions: forward, reverse, and breakdown • a simple but effective model of the diode i-v characteristic in the forward direction: the constant-voltage-drop model Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**Introduction**• a powerful technique for the application and modeling of the diode (and in later chapters, transistors): dc-biasing the diode and modeling its operation for small signals around the dc-operating point by means of the small-signal model • the use of a string of forward-biased diodes and of diodes operating in the breakdown region (zener diodes), to provide constant dc voltages (voltage regulators) • application of the diode in the design of rectifier circuits, which convert ac voltages to dc as needed for powering electronic equipment • a number of other practical and important applications Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**ideal diode – most fundament nonlinear circuit element**two terminal device circuit symbol shown to right operates in two modes on and off 4.1.1. Current-VoltageCharacteristic of the Ideal Diode Figure 4.1: Diode characteristics Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**4.1.1. Current-VoltageCharacteristic**• cathode –negative terminal, from which current flows • anode – positive terminal of diode,into which current flows • voltage-current (VI) behavior is: • piecewise linear for rated values • nonlinear beyond this range Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**ideal diode: is most fundament nonlinear circuit element**two terminal device with circuit symbol to right operates in two modes forward and reverse bias 4.1.1: Current-VoltageCharacteristic of the Ideal Diode mode #2: reverse bias = open ckt. mode #1: forward bias = short ckt device symbol with two nodes figure 4.1. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**External circuit should be designed to limit…**current flow across conducting diode voltage across blocking diode Examples are shown to right… 4.1.1. Current-VoltageCharacteristic Figure 4.2: The two modes of operation of ideal diodes and the use of an external circuit to limit (a) the forward current and (b) the reverse voltage. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**One fundamental application of this piecewise linear**behavior is the rectifier. Q:What is a rectifier? A: Circuit which converts AC waves in to DC…ideally with no loss. 4.1.2: A Simple Application – The Rectifier Figure 4.3(a): Rectifier Circuit Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**This circuit is composed of diode and series resistor.**Q:How does this circuit operate? A: The diode blocks reverse current flow, preventing negative voltage across R. 4.1.2: A Simple Application – The Rectifier Figure 4.3(a): Rectifier Circuit Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**Consider the circuit of Figure 4.4. A source (vS) with peak**amplitude of 24V is employed to charge a 12V dc-battery. Q(a):Find the fraction of each cycle during which the diode conducts. Q(b):Find peak value of diode current and maximum reverse-bias voltage that appears across the diode. Example 4.1:Diode Rectifier Figure 4.4: Circuit and Waveforms for Example 4.1. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**Q: How may diodes be used to create logic gates?**A: Examples of AND / OR gates are shown right. Refer to next slide. 4.1.3. Another Application,Diode Logic Gates Figure 4.5: Diode logic gates: (a) OR gate; (b) AND gate (in a positive-logic system). Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**OR GATE**AND GATE IFvA = 5VTHEN diodeA will conduct ANDvY = vA = 5V IFvA = 0VTHEN diodeA will conduct ANDvY = vA = 0V IF all diodes block THENvY = 5V + 5V - + 5V- IF any diode conducts THENvY = 5V Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**Q: What difficulties are associated with multi-diode**circuits? A: Circuit cannot be solved without knowledge of diodes’ statuses. Yet, statuses are dependent on the solution. Example 4.2:More Diodes To apply nodal / mesh techniques, one must have knowledge of all component impedances. Figure 4.4: Circuit and Waveforms for Example 4.1. Figure 4.6: Circuits for Example 4.2. IFvB < 0 THENZD1 = 0ohmsELSEZD1 = open circuit Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**Example 4.2:More Diodes**• Q: How does one solve these circuits? • A: One must use the following steps… • 1) assume the status of all diodes • 2) solve via mesh / nodal analysis • 3) check for coherence Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**Example 4.2:More Diodes**If answer to either of these is no, then the solution is notphysically realizable. • Q: How does one check for coherence? • A: One must ask the following questions… • 1) Are calculated voltages across all “assumed conducting” diodes forward-biased? • 2) Are the calculated currents through all “assumed blocking” diodes zero? • Q: What does one do, if the solution is not coherent? • A: One must change one or more of these assumptions and solve as well as check for coherence again. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**Most common implementation of a diode utilizes pn junction.**I-V curve consists of three characteristic regions forward bias: v > 0 reverse bias: v < 0 breakdown: v << 0 4.2. Terminal Characteristicsof Junction Diodes discontinuity caused by differences in scale Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**4.2.1. TheForward-Bias Region**• The forward-bias region of operation is entered when v > 0. • I-V relationship is closely approximated by equations to right. (4.3) is a simplification suitable for large v Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**4.2.1. TheForward-Bias Region**• Equation (4.3) may be reversedto yield (4.4). • This relationship applies over as many as seven decades of current. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**4.2.1. TheForward-BiasRegion**• Q:What is the relative effect of current flow (i) on forward biasing voltage (v)? • A: Very small. • 10x change in i, effects 60mV change in v. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**cut-in voltage – is voltage, below which, minimal current**flows approximately 0.5V fully conducting region –is region in which Rdiode is approximately equal 0 between 0.6 and 0.8V 4.2.1: TheForward-BiasRegion fully conducting region Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**Example 4.3**• Refer to textbook… Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**4.2.2. The Reverse-Bias Region**• The reverse-bias region of operation is entered when v < 0. • I-V relationship,for negative voltages with |v| > VT (25mV), is closely approximated by equations to right. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**4.2.2. The Reverse-Bias Region**• A “real” diode exhibits reverse-bias current, although small, much larger than IS . • 10-9 vs. 10-14Amps • A large part of this reverse current is attributed to leakage effects. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**The breakdown region of operation is entered when v < VZK.**Zener-Knee Voltage (VZK) This is normallynon-destructive. 4.2.3. The Breakdown Region breakdown region Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**V = -VZK**V = -VT V =10VT Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**4.3. Modeling the Diode Forward Characteristic**• The previous slides define a robust set of diode models. • Upcoming slides, however, discuss simplified diode models better suited for use in circuit analyses: • exponential model • constant voltage-drop model • ideal diode model • small-signal (linearization) model Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**4.3.1. The Exponential Model**• exponential diode model • most accurate • most difficult to employ in circuit analysis • due to nonlinear nature Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**4.3.1. The Exponential Model**• Q: How does one solve for ID in circuit to right? • VDD = 5V • R = 1kOhm • ID = 1mA @ 0.7V • A:Two methods exist… • graphical method • iterative method Figure 4.10: A simple circuit used to illustrate the analysis of circuits in which the diode is forward conducting. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**step #1:Plot the relationships of (4.6) and (4.7) on single**graph step #2:Find intersection of the two… load line and diode characteristic intersect at operating point 4.3.2. Graphical Analysis Using Exponential Model Figure 4.11: Graphical analysis of the circuit in Fig. 4.10 using the exponential diode model. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**Pro’s**Intuitive b/c of visual nature Con’s Poor Precision Not Practical for Complex Analyses multiple lines required 4.3.2. Graphical Analysis Using Exponential Model Figure 4.11: Graphical analysis of the circuit in Fig. 4.10 using the exponential diode model. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**step #1: Start with initial guess of VD.**VD(0) step #2: Use nodal / mesh analysis to solve ID. step #3: Use exponential model to update VD. VD(1) = f(VD(0)) step #4:Repeat these steps until VD(k+1) = VD(k). Upon convergence, the new and old values of VD will match. 4.3.3. Iterative Analysis Using Exponential Method Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**4.3.3. Iterative Analysis Using Exponential Method**• Pro’s • High Precision • Con’s • Not Intuitive • Not Practical for Complex Analyses • 10+ iterations may be required Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**Q: How can one analyze these diode-based circuits more**efficiently? A: Find a simpler model. One example is assume that voltage drop across the diode is constant. 4.3. Modeling the Diode Forward Characteristic Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**The constant voltage-drop diode model assumes that the slope**of ID vs. VD is vertical @ 0.7V Q:How does example 4.4 solution change if CVDM is used? A: 4.262mA to 4.3mA 4.3.5. TheConstant Voltage-Drop Model Figure 4.12: Development of the diode constant-voltage-drop model: (a) the… Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**The ideal diode model assumes that the slope of ID vs. VD is**vertical @ 0V Q:How does example 4.4 solution change if ideal model is used? A: 4.262mA to 5mA 4.3.6. IdealDiode Model Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**ideal diode: is most fundament nonlinear circuit element**two terminal device with circuit symbol to right operates in two modes forward and reverse bias 4.1.1: Current-VoltageCharacteristic of the Ideal Diode mode #2: reverse bias = open ckt. mode #1: forward bias = short ckt device symbol with two nodes figure 4.1. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**exponential model**low voltages less complex circuits emphasis on accuracy over practicality constant voltage-drop mode: medium voltages = 0.7V more complex circuits emphasis on practicality over accuracy ideal diode model high voltages >> 0.7V very complex circuits cases where a difference in voltage by 0.7V is negligible small-signal model this is next… When touse these models? Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**4.3.7. Small-Signal Model**• small-signal diode model • Diode is modeled as variable resistor. • Whose value is defined vialinearization of exponential model. • Around bias point defined by constant voltage drop model. • VD(0) = 0.7V Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**4.3.7. Small-Signal Model**Neither of these circuits employ the exponential model – simplifying the “solving” process. • Q:How is the small-signal diode model defined? • A: The total instantaneous circuit is divided into steady-state and time varying components, which may be analyzed separately and solved via algebra. • In steady-state, diode represented as CVDM. • In time-varying, diode represented as resistor. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**CVDM**Total Instantaneous Solution (vD.) DC Steady-State Solution (VD.) DC = + AC Time-Varying Solution (vd.) AC Figure 4.14: (a) Circuit for Example 4.5. (b) Circuit for calculating the dc operating point. (c) Small-signal equivalent circuit. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**Q:How is the small-signal diode model defined?**step #1: Consider the conceptual circuit of Figure 4.13(a). DC voltage (VD) is applied to diode Upon VD, arbitrary time-varying signal vd is super-imposed 4.3.7. Small-Signal Model Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**DC only – upper-case w/ upper-case subscript**time-varying only – lower-case w/ lower-case subscript total instantaneous – lower-case w/ upper-case subscript DC + time-varying 4.3.7. Small-Signal Model Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**4.3.7. Small-Signal Model**• step #2: Define DC current as in (4.8). • step #3: Define total instantaneous voltage (vD) as composed of VD and vd. • step #4: Define total instantaneous current (iD) as function of vD. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**4.3.7. Small-Signal Model**• step #5:Redefine (4.10) as function of both VD and vd. • step #6: Split this exponential in two. • step #7:Redefine total instant current in terms of DC component (ID) and time-varying voltage (vd). Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**4.3.7. Small-Signal Model**• step #8: Apply power series expansion to (4.12). • step #9: Because vd/VT << 1, certain terms may be neglected. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**4.3.7. Small-Signal Model**• small signal approximation • Shown to right for exponential diode model. • total instant current (iD) • small-signal current (id.) • small-signal resistance (rd.) • Valid for for vd < 5mV amplitude (not peak to peak). Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**4.3.7. Small-Signal Model**• This method may be used to approximate any functiony = f(x) around an operating point (x0, y0). Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**4.3.7: Small-Signal Model**• Q:How is small-signal resistancerd defined? • A: From steady-state current (ID) and thermal voltage (VT) as below. • Note this approximation is only valid for small-signal voltages vd < 5mV. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**Example 4.5:Small-Signal Model**• Consider the circuit shown in Figure 4.14(a) for the case in which R = 10kOhm. • The power supply V+ has a dc value of 10Vover which is super-imposed a 60Hz sinusoid of 1V peak amplitude (known as the supply ripple) • Q: Calculate both amplitude of the sine-wave signal observed across the diode. • A:vd.(peak) = 2.68mV • Assume diode to have 0.7V drop at 1mA current. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)**Figure 4.14: (a) circuit for Example 4.5. (b) circuit for**calculating the dc operating point. (c) small-signal equivalent circuit. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)